3 days ago · A sphere with radius r r has a volume of \frac {4} {3} \pi r^3 34πr3 and a surface area of 4 \pi r^2 4πr2. A sphere has several interesting properties, one of which is that, of all shapes with the same surface area, the sphere has the largest volume.

Divide each term in 4πr2 = S 4 π r 2 = S by 4π 4 π and simplify. Tap for more steps... Take the specified root of both sides of the equation to eliminate the exponent on the left side. Simplify ±√ S 4π ± S 4 π. Tap for more steps... The complete solution is the result of both the positive and negative portions of the solution. Tap for more steps...

Surface Area of Sphere = 4πr², where r is the radius of sphere. A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre. In other words, a sphere is a perfectly round geometrical object in three-dimensional space, just like a surface of a round ball.

Dec 1, 2018 · Some of you may have seen in school that the surface area of a sphere is 4\pi R^2 4πR2, a suspiciously suggestive formula given that it’s a clean multiple of \pi R^2 πR2, the area of a circle with the same radius. But have you ever wondered why is this true? And I don’t just mean proving this 4\pi R^2 4πR2 formula.

One geometric explanation is that $4\pi r^2$ is the derivative of $\frac{4}{3}\pi r^3$, the volume of the ball with radius $r$, with respect to $r$. This is because if you enlarge $r$ a little bit, the volume of the ball will change by its surface times the small enlargement of $r$.

We have that the surface area formula is: SA = 4\pi r^2 If we take the derivative with respect with time, we get: \frac{dSA}{dt} = 8\pi r \frac{dr}{dt} Now, from the problem we are given that ...

Aug 3, 2023 · The surface area of a sphere is the total area covered by its curved surface. The Surface Area of a Sphere Formula is given by \(4\pi r^2\). The surface area of a sphere is always expressed in square units, such as square centimeters (cm²) or square meters (m²).

Nov 15, 2017 · 4pir 2 is the first derivative of the formula for the volume of a sphere: 4pir 3 / 3. This sorta makes sense if you think of an infinitely small rise in r as being a infinitely-thin shell around the sphere, which is what the surface area is.

The surface area of a sphere can be found using the formula 4pir², where r is the radius of the sphere. This formula is derived from the fact that a sphere is made up of an infinite number of flat faces (or “patches”), each of which has an area equal to 4pir².